If \(\rm x+y=\frac{\pi}{4}\), then the value of (1 + tan x)(1 + tan y)

If \(\rm x+y=\frac{\pi}{4}\), then the value of (1 + tan x)(1 + tan y) is:

Answer» Correct Answer - Option 3 : 2

Concept:

Trigonometric Identities:

\(\rm \tan(A\pm B)=\frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}\).

Calculation:

Given that \(\rm x+y=\frac{\pi}{4}\).

⇒ \(\rm \tan(x+y)=\tan \frac{\pi}{4}\)

⇒ \(\rm \frac{\tan x + \tan y}{1 -\tan x \tan y}=1\)

⇒ tan x + tan y = 1 - tan x tan y ... (1)

Now, (1 + tan x)(1 + tan y)

= 1 + tan y + tan x + tan x tan y

Using the value in equation (1), we get:

= 1 + 1 - tan x tan y + tan x tan y

= 2.

**Trigonometric Formula:**
sin (A ± B)	sin A cos B ± sin B cos A
cos (A ± B)	cos A cos B ∓ sin A sin B
tan (A ± B)	\(\rm \dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}\)
cot (A ± B)	\(\rm \dfrac{\mp1+cot A\cot B}{\pm\cot A+\cot B}\)